Friday, November 14, 2008

Elearn Geometry Problem 205: Right Triangle Area, Exradii

Right triangle

See complete Problem 205 at:
gogeometry.com/problem/p205_right_triangle_area_exradii.htm

Right Triangle Area, Excircles, Exradii relatives to legs or catheti. Level: High School, SAT Prep, College geometry

Post your solutions or ideas in the comments.

4 comments:

  1. we know that Tan A/2= S/p(p-a)where S is the area of trABC and p is the semiperimeter but here angle A=90 so S/p(p-a)= Tan 45=1 so S=p(p-a) and we know rb=S/(p-b) , rc=S/(p-c) so rb.rc=S^2/(p-b)(p-c)=p(p-a)=S HENCE rb.rc=S

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  2. Solution of problem 205.
    Let be s the semiperimeter of ABC, and r the inradius. From problem 200, r = s – a. From problem 202, rb = s – c and rc = s – b.
    So we have S = sr = s(s – a) and
    S.rb.rc = s(s – a)(s – b)(s – c) = S^2 (from Heron’s theorem). Hence S = rb.rc.

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  3. To Antonio:
    The link to problem 206 always leads to problem 205 instead. Could you fix it?
    Thanks.

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    Replies
    1. Nilton, what is the url of the web page with the link to problem 205?
      Thanks

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